Spintronics of helical edge states interacting with a quantum magnet

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The existence of helical edge states is a key feature of a two-dimensional topological insulator. These edge states are immune against single-particle backscattering in the absence oftime-reversal symmetry breaking felds. Placing a magnetic insulator in proximity to the helical edge states, the Exchange field will open a gap in the helical edge state spectrum.Surprisingly, when the magnet has its own dynamics with a properly aligned easy-plane anisotropy, the application of a voltage bias sets the magnet in a precessional mode in which the magnet pumps charge in such a way that the quantized quantum spin Hallconductance is restored, in spite of the presence of a gap in the excitation spectrum of the helical edge. This leads to intriguing transport and noise properties, and was proposed to bea platform for the realization of an adiabatic quantum motor.Building on our previous joint work [Silvestrov, Recher, and Brouwer, Phys. Rev. B 93, 205130 (2016)], we here propose to extend the study of this remarkable system into new directions,such as thermoelectric effects, and consider aspects beyond the idealized model description used in previous publications by us and others. Specifically, in a first set of subprojects we address thermoelectric applications of an easy-plane magnetic insulator exchange-coupled to a helical edge, and device applications such as "thermomagnetization", a "thermal quantum Motor", and a mesoscopic "electron cooler". Other directions of research here include nonlinear transport, low frequency noise and magnetization fluctuations as well as quantum interference effects. The second half of the proposal will be devoted to generalizations of theidealized model. We plan to use the Landau-Lifshitz equation for the description of the current/bias driven dynamics of a Setup with less symmetries than in the original publications. New interesting features in current-voltage characteristics and magnetization dynamics are expected. Other proposed Problems include the case of a magnet with several degrees of freedom and a metallic magnet.